Deprojection of galaxy cluster X-ray, Sunyaev-Zeldovich temperature decrement, and weak-lensing mass maps

A general method of deprojecting two-dimensional images to reconstruct the three-dimensional structure of the projected object (specifically, X-ray, S unyaev-Zeldovich [SZ], and gravitational lensing maps of rich clusters of g alaxies), assuming axial symmetry, is considered. Here we test the applicab ility of the method for realistic, numerically simulated galaxy clusters, v iewed from three orthogonal projections at four redshift outputs. We demons trate that the assumption of axial symmetry is a good approximation for the three-dimensional structure in this ensemble of galaxy clusters. Applying the method, we demonstrate that a unique determination of the cluster incli nation angle is possible from comparison between the SZ and X-ray images an d, independently, between SZ and surface density maps. Moreover, the result s from these comparisons are found to be consistent with each other and wit h the full three-dimensional structure inclination angle determination. The radial dark matter and gas density profiles as calculated from the actual and reconstructed three-dimensional distributions show a very good agreemen t. The method is also shown to provide a direct determination of the baryon fraction in clusters, independent of the cluster inclination angle.